If you didn’t see Burton and Taylor (BBC Four, Monday), look at the photo of Dominic West and Helena Bonham Carter, above, as the famous Hollywood couple. Glamorous, aren’t they? And instantly recognisable as Richard and Elizabeth, although maybe she more than he.

West doesn’t quite exude the same garrulous machismo that Burton did, which was a foil for Taylor’s blowsy femininity. And that’s how it played out on screen in this feature-length biopic. Bonham Carter got Taylor down perfectly in all her guises, from vulnerable to flirty to brawling; West, meanwhile, has a way of capturing a real-life character (he was terrifying as mass murderer Fred West) without having to tick every box. It was set in the early 1980s when the pair, who had been divorced from each other twice, and had been estranged for five years, reunited to appear in a Broadway production of Private Lives. Both of their careers, but not their fame, were on the wane.

Taylor, bleary from her addiction to pills and booze, was a co-producer, and she wanted to reel in the love of her life, Burton. He was attempting sobriety, about to be married and anxiously awaiting the green light on his life’s ambition, a production of King Lear.

Private Lives was a huge commercial success. The audience wasn’t there to see Noël Coward’s comedy about an abusive codependent divorced couple, honeymooning with their new spouses in the same hotel. They wanted the Liz and Dick show, and hooted loudly every time they spotted a parallel between the onstage story and what they knew – and everyone knew all the details – about the famously fiery Burton-Taylor relationship.

“They thought they had an invite into our lives, to see it happen in front of them,” said Burton, horrified by the reality of the situation he had landed himself in – for $70,000 a week.

Taylor relished the adulation, ad-libbing to the audience and appearing with a parrot on her shoulder to upstage Burton after a pre-show bust-up.

The drama – it had great material to work with – captured the pair’s intensely damaging relationship but also the sheer fun they had, and how much they loved each other. Irish actor Stanley Townsend as Milton, the play’s American director, conveyed the weary resignation of trying to get an old-school star such as Taylor to do anything she didn’t want to. When the critics slated Private Lives, Burton consoled an upset Taylor, saying: “Critics deserve nothing but our pity. So close to art and yet they contribute absolutely nothing whatsoever towards it. It’s like being a eunuch at an orgy.” Right, then.

Taking Care of Business, (RTÉ One, Thursday) is another series about companies in trouble – a sign of the times, obviously, but this one is more serious than RTÉ’s recent The Takeover. There the staff came up with the solutions, but for the businesses in this series, the bank problems loom large, and the difficulties have gone way past jokey fixes.

The constants in each episode are business consultants Sean Dunne and Tommy Murphy, and of course the first disappointment is that it’s not that Sean Dunne, Baron of Ballsbridge. Now that would be an instructive business programme. This Dunne is, like Murphy, an accountant, and he’s clear-eyed and quietly spoken. You’d like him batting for you.

Kudos is due to the programme makers for starting the series with an unglamorous but highly representative business story. James Fegan is the third generation to run the family food-distribution business – or, as he says, “moving boxes from one place to another”. He expanded the business in 2007, borrowing €3.5 million to build a massive warehouse in Finglas, and €1.5 million for a house.

And then business faltered. He supplies restaurants and shops; as their trade slumped, so did his. Some went under, so bad debts piled up. Asked how it has been going, he said, “It’s, oh, it’s bollix, is the best word I can use,” his stressed face telling more than he could. He was candid about how the years of drowning in debt has impacted on his mental health, as was his wife when interviewed at home. That sort of openness will surely help viewers who are in a similar situation.

Midway through the process the banks closed in, putting his building into receivership. “It’s just a new landlord for the building,” said Murphy, giving perspective to the situation, which seemed like the advisers’ most valuable role. They urged Fegan to get back to the day-to-day business of selling, meeting customers, and advised him to avoid in his office (“the bunker”) while getting deeper into despair about the scale of the debt.

No figures were picked apart, which is frustrating in a show about business survival. We didn’t see much of the fixing and negotiating that went on behind the scenes – and that would have been good – but Taking Care of Business, which ended on a positive note from a newly invigorated Fegan, did give a good insight into a bad situation.

When Christopher Guest made This is Spinal Tap, he helped create the mockumentary, a genre that has successfully transferred to TV, with such comedy gold examples as The Office, Parks and Recreation and Modern Family. So his UK TV debut, Family Tree (BBC Two, Tuesday), a HBO-BBC collaboration, came with the high expectation of something if not hilarious, then at least several inventive notches above your average sitcom. Which it wasn’t.

The plot – loose to allow for multiple eccentrics to pop up for brief turns – revolves around hangdog loser Tom Chadwick (Chris O’Dowd – he could do this in his sleep) tracing his family tree. His bonkers sister Bea (Nina Conti) is a ventriloquist who expresses her feelings through her hand puppet, Monkey. Tom’s father is obsessed with 1970s racist and sexist sitcoms and is married to a dislikable eastern European woman.

Family Tree was unscripted, and while the actors sometimes came up with amusing lines, it just showed that improvisation can be as stilted and forced as any script. They threw everything at it, including the corniest slapstick, but got no laughs. This week, in the second episode, Tom discovered his grandfather was the back end of a pantomime horse, so he and sidekick Pete (Tom Bennett, the funniest character, and the least self-conscious) took part in a pantomime-horse race. Even that didn’t work. All curiously unfunny.

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